Panel Data Research Center at Keio University
DISCUSSION PAPER SERIES
DP2013-003
August, 2013

The Impact of the Designated Manager System of Japanese Public Halls:
Measuring Technical, Allocative, and Productive Effeciency

Miyuki Taniguchi＊【Abstract】

This paper attempts to measure how the productive efficiency of Japanese publichalls has changed following the introduction of the Designated Manager System(DMS). The DMS which was introduced for public halls around 2006 was intended
to introduce market mechanisms into the public sector. In particular, we
hypothesize that the DMS has forced the managers of public halls to be more cost
conscious, leading to an improvement of the soft budget problem. That is, theproduction possibility frontier function for public halls is expected to shift outwards,
and production inefficiencies would be smaller as a result of the introduction of the
DMS. An unbalanced panel data set from 2004 to 2009 on 200, roughly 10 % of thetotal number of public halls, randomly chosen public halls was used to estimate astochastic production frontier. It is found that the introduction of the DMS did leadto an upward shift of the production frontier, but it did not lead to any large change
in the efficiency of production.

＊

Graduate School of Economics, Keio University

Panel Data Research Center at Keio University
Keio University

The Impact of the Designated Manager System of Japanese Public Halls:
Measuring Technical, Allocative, and Productive Efficiency Miyuki Taniguchi†
Graduate School of Economics
Keio University

Abstract
This paper attempts to measure how the productive efficiency of Japanese publichalls has changed following the introduction of the Designated Manager System(DMS).

The DMS which was introduced for public halls around 2006 was intended

to introduce market mechanisms into the public sector.

In particular, we

hypothesize that the DMS has forced the managers of public halls to be more cost
conscious, leading to an improvement of the soft budget problem.

That is, theproduction possibility frontier function for public halls is expected to shift outwards,
and production inefficiencies would be smaller as a result of the introduction of theDMS.

An unbalanced panel data set from 2004 to 2009 on 200, roughly 10 % of thetotal number of public halls, randomly chosen public halls was used to estimate astochastic production frontier.

It is found that the introduction of the DMS didlead to an upward shift of the production frontier, but it did not lead to any largechange in the efficiency of production.
Keywords: allocative efficiency, data envelopment analysis, designated manager system,
productive efficiency, technical efficiency, stochastic frontier analysis.
JEL Classification Codes: H76, H32, D24

The author would like to thank Masaru Kaneko, Taisuke Katayama, Colin McKenzie, andTamon Yamada for their helpful comments and suggestions.
† Address for correspondence: Graduate School of Economics, Keio University, 2-15-45

Mita, Minato-ku, Tokyo, JAPAN, 108-8345.
+81-3-5427-1578. E-mail: miyuki@z3.keio.jp
1

Phone: +81-3-5427-1831.

Fax:

1. Introduction
In order to improve the financial inefficiencies in public sector by utilizing thevitality of the private sector, New Public Management (NPM) has started in the United
Kingdom and New Zealand in 1980s.

Similarly, the Koizumi Government undertook

structural reforms from 2001 to try to solve the soft budget problem in the public sector.
As a result, Japan moved towards a smaller government and some parts of the public
sector were privatized. The introduction of the Designated Manager System (DMS) for
certain public facilities is one part of these structural reforms.

The three main

purposes of the DMS were: to reduce the public deficit; to reduce the covering of the
deficits of the public facilities by local governments after losses have been incurred; andto introduce private management methodologies into public facilities. Public facilities
that became the subject of the DMS include: public facilities for art and culture,sewerage disposal plants, airports, gymnasia and libraries.

The DMS is related to an

Article 244 of the Local Autonomy Law (Chihouzichi Hou), “public facilities (Ooyake no

Shisetsu)”. In order to enable all public facilities to select the private manager as
designated managers, the Article 244 of the Local Autonomy Low was changed in June
6, 2003 and enacted among several public halls in September 2, 2003.

Then, theArticle 244 of the Local Autonomy Law entirely enacted among the other public halls in
September 3, 2006. (Local Autonomy Act 244)

Therefore, it can be said that the DMS

was introduced into public halls in 2006.
No Japanese law defines what public hall is. Generally, it was considered that
there was a lot of wasteful expenditure associated with Japanese public halls (forexample, Kobayashi (2006), P.P. 24 - 26), so it was rather natural that the DMS wasapplied to public halls as well. In this paper, the definition of a “public hall” is any
facility which belongs to the Association of Public Theaters and Halls in Japan(Zenkoku Kouritsu Bunka Shisetsu Kyougikai, also known as Kou Bunn Kyou), andincludes, for example, community centers, music halls, all-purpose halls, theaters, andlibraries with halls. The number of public halls in Japan increased rapidly following
the expansionary Keynesian fiscal policy of the 1990s. This increase in the number ofpublic halls was considered as having the merit of providing a “fairer” distribution of art
and cultural goods, not only for people living in city areas, but also for those people
living in country areas. A potential disadvantage of this policy was an increase in theinefficiency in the public sector.

Since 2000, the construction of public halls has

continued, and there are now about 2200 facilities in total.
This paper aims to assess the economic effect of the introduction of the DMS on
2

Japanese public halls by estimating an efficiency indicator.

There are three areas ofexisting research that are related to this paper: general assessments of the
management of public facilities; research related to the DMS system; and themeasurement of inefficiency via the estimation of a production possibility frontier, .
There are several papers evaluating the management of public facilities likepublic libraries, public theaters or university libraries using some sort of efficiency
approach like a Stochastic Frontier Approach (SFA) and/or a Data Envelopment
Approach (DEA) (see, for example, Tamura (2002), Reichmann (2004) and Last andWetzel (2009)).. Important issues in this research are how to define the “output” of the
public facility, and how to take account of any positive externalities associated with thefacility. There are examples where the output of a facility is treated as the utilities ofconsumers, and the Contingent Valuation Method (CVM) is used to measure positive
externalities.

Some examples of research measuring inefficiency in the public sector

via SFA &/or DEA approaches include: Tamura’s (2002) application to book lending inJapanese public libraries, and which interestingly enough included the number ofvolunteers as one of inputs because there are a sizeable number of volunteers inJapanese public libraries; Reichmann’s (2004) application to university libraries inGermany, Austria, Switzerland, the United States, Australia, and Canada; and Last
and Wetzel’s (2009) application to German public theaters.

These three papers

examined the existence of inefficiencies and measured them.
Rather than providing data based on evaluations, many of the existing studies of
the Japanese DMS tend to discuss ideological matters.

Nakaya (2005) summarized thesituation facing public halls before the DMS was introduced, and pointed to theimportance of assessing the work of designated managers after the DMS was introduced
Nakaya’s (2005) book has become a kind of handbook for local governments and art
managers. From the view point of political sociology, Kobayashi (2006) pointed out thedifficulties in assessing the activities in the cultural sector and considered the problems
that might arise after the introduction of the DMS. Cultural Policy Network edi.
(2004) estimated the changes in public cultural facilities in Japan after the introductionof the DMS. Kobayashi (2006) writing right at the time the DMS was introduced
expressed negative opinions concerning economic assessments of public facilities via
economic indicators because they think that the public facilities for art and culture havesome value which are not measurable by economic indicators.

Nakagawa andMatsumoto (2007) also expressed their negative opinion against the assessment of the
DMS using economic techniques. While this is certainly true, policies for art andculture that totally ignore profit or cost considerations are unrealistic.
3

There are noexisting studies which evaluate the introduction of the DMS to pubic halls.

Using

economic indicators can be very useful when drafting realistic policies with regard to
the cost of these facilities.

This is the first attempt to measure the efficiencies of publichalls before and after the DMS.
The third and final area of related research focuses on measuring inefficiency offirms via the estimation of a production function.

The econometric methods used areparametric, semi-parametric, and non-parametric approaches.

The standard

parametric approaches are known as Stochastic Frontier Analysis (SFA) and Corrected
Ordinary Least Squares, (COLS), while the standard non-parametric approach is
known as Data Envelopment Analysis (DEA). This study uses both the parametric
SFA and the non-parametric DEA approaches, and measures technical, allocative andproductive inefficiencies.

SFA was developed by Aigner et al. (1977) and Meeusen andvan den Broeck (1977) in the economics area, while DEA is developed by Charnes et al.
(1978) in an operations research context.

Given their respective advantages anddisadvantages, SFA and DEA can be viewed as being complementary. For instance,
one of the key disadvantages of DEA is that it does not allow for hypothesis testing
whereas SFA does. One of the disadvantages of SFA is the need to assume a specificform for the productive function and a specific distribution for the inefficiency
component, while DEA does not require these assumptions.

Combining the threeinefficiency indicators proposed by Farell (1957) with SFA or DEA enables inefficiency
decompositions to be undertaken.
It is worth noting that the measurement of inefficiency is usually undertaken forfirms in the private sector, but there are examples of applications to the public sector.
For example, Nakayama (2002) measures inefficiency in the water processing andsewerage in Japan, via both SFA and DEA, Goto (2002) measures the efficiency of theelectric industry, especially the electricity supply network, in the United States via SFA.
The key contributions of this paper are the construction of a unique data set forJapanese public halls; the estimation of a production function for Japanese public halls;
and the measurement of the productive, technical, and allocative efficiencies ofJapanese public halls via both SFA and DEA.

This is the first application of SFA andDEA to public halls in Japan.
The rest of this paper is organized as follows. Section 2 presents the backgroundrelating to why the DMS was introduced for public halls in Japan.

In this section,

Section 3 provides an explanation of the methodology used to measure inefficiencies.
Section 4 gives detail of the data used in this paper. Section 5 presents the empiricalresults. Section 6 contains some concluding remarks. An Appendix provides a simple
4

econometric model to explain the relationship between the public financial power of
local government authorities and their selection of the DMS.

2. The Introduction of the DMS for Japanese Public
Halls
Prior to the introduction of the DMS, the Entrusted Manager System (EMS)
existed. The EMS enables a local government to choose either the direct managementof a public facility or the management of the facility by an extra-governmentorganization of the local government. The EMS has a less characteristic of the New
Public Management than DMS.

The key difference between the EMS and the DMS isthat the DMS enables private managers to be employed to manage the public halls.

In

2006, the DMS introduced to public halls except the case of the testing introduction.
One of the important purposes of the introduction of the DMS is to reduce the financial
deficits of local governments in Japan.

Before the introduction of the DMS, local

governments cover the deficits for the management of public halls. That is the reason
why the managers of public halls were not conscious of costs and there were a lot of
inefficient managements in public halls.

However, by adopting the management

methods of the private sector, the facilities may become more cost conscious. Even if
the managers of a facility do not change, the management of public halls has potentiallychanged because the DMS has also fixed or reduced the budgets for public halls.

Thus,

the DMS can make the management of public sector more efficient.
Table 1 shows that by 2007 about 34% of the facilities for art and culture
introducing the DMS in 2007.

To be more concrete, there were about 2700 facilities

that were managed directly, and about 1300 facilities which had introduced the DMS by
2007. As shown in Table 2, the facilities which had previously introduced the EMS
also tend to be those that have introduced the DMS, while the facilities which had been
under direct management by the local government tend to have not introduced the DMS.
In many cases, the switch from the EMS to the DMS has not result in a change in the
manager of the facility from a local government or their affiliated organizations to
private organization.

5

Table 1: Adoption of Designated Manager System by Public Facilities for the Arts andCulture (includes not only public halls but also other public cultural facilities)
Percentage ofManager Type

Facilities
Adopting

PublicNon-public

DMS
Prefectural facilities

68.9%

65%

35%

Facilities of Cities Designated by Ordinance

79.2%

61%

39%

28.2%

27%

73%

34.2%

37%

63%

Facilities of Municipalities except Cities
Designated by Ordinance
Total

Notes: The total number of facilities is 4,265.

After the elimination of facilities that did not

answer the survey or provided unclear answers, the sample size is 4,177.

This sample

includes not only public halls, but also other public facilities for the arts and culture.
Source: This table was constructed using survey data reported in i Japan Foundation for
Regional Art-Activities (2007)

6

Table 2: Impact of the Introduction of the Designated Manager System for Public Facilities
for Art and Culture; By Management Type

Pre-DMS

Post-DMS

Public/Non-Public
DivisionManagement

NumberType

DirectManagement

2782

Management

NumberType(Percentage)

Direct2636

Management(94.8%)

Designated146

Manager(5.2%)

Public2636(100.0%)Public83(56.8%)

Non-public

63(43.2%)

EntrustedManager1279

Direct78

Management(6.1%)

Designated1201

Manager(93.9%)

Public78(100.0%)Public410(34.1%)

Non-public

791(65.9%)

New

116

Direct57

Management(49.1%)

Designated59

Manager(50.9%)

Public57(100.0%)Public35(59.3%)

Non-public

24(40.7%)

Source: as for Table 1

The results presented in Appendix 1 indicate the financial power of the local
government controlling the facility is a good explanatory of whether or the facility
adopts the DMS, and, in particular, show that local governments with strong financial
positions tend to be the ones that adopt the DMS for their facilities.

This result

implies that the local governments which have weak financial power tend not to
introduce the DMS.
7

3. Method
In order to examine the impact of the DMS on public halls, we estimate a production
function for these facilities that allows for inefficiencies. This production function isestimated using both the SFA and DEA approaches. Given estimates of these production
functions, it is then possible to compute the inefficiency indicators proposed by Farell(1957).
3. 1 Farell’s (1957) Definition of (In)-Efficiency
The idea of inefficiency indicators was first proposed by Farell (1957) and his method
has become the most popular method of measuring inefficiency.
is shown clearly by Kopp and Diewert (1982).

This decomposing way

Farrell classifies inefficiencies into three

types: technical efficiency (TE), allocative efficiency (AE), and productive efficiency (PE).
A simple example, assuming two inputs and one output case, is used to illustrate thesethree concepts. Both Figure 1 and 2 shows a frontier unit isoquant for technology (SS’)
and a point of inefficient activity denoted bydoes not lie on SS’. The point.

is obviously inefficient because it

is defined as a point of intersection of the line segmentwith the isoquant curve SS’. The line segment PP’ is denoted as the minimum
isocost line which goes through the most efficient point denoted by. The point

is defined as the point of the intersection of the line segmentwith the line segment

PP’.

which achieves mostis a point that achieves the same minimum cost as

efficient allocation of input.

In this case, Farell’s (1957), three efficiency indicators,

technical efficiency (TE), allocative efficiency (AE), and productive efficiency (PE), aredefined as follows:
(1)
(2)
.

(3)

While Figure 1 presents the case of a smooth frontier unit isoquant for technology (SS’),
Figure 2 illustrates the case where the frontier unit isoquant for technology (SS’) is aseries of line segments (as is generated by DEA analysis).
8

Figure 1 and Figure showsthat how to decompose PE into TE and AE is the same in both SFA and DEA.
Figure 1: Definition of Inefficiency Indicators via SFA

X1

isoquant
XA

S

P
XB
XC
XE
S’
P’

0

isocost9

X2

Figure 2: Definition of Inefficiency Indicators for Input-Orientated DEA

X1/Y

isoquant
XA

S

P




XB



XC


XE

S’



P’

0

X2/Y

isocost3. 2 Using SFA to Measure Efficiency
The basic idea for the measurement of efficiency indicators obtained using Stochastic
Frontier Analysis (SFA) and using input-orientated Data Envelopment Analysis (DEA)
is essentially the same. That is why Nakayama (2002) measured the three kinds ofinefficiencies of the waterworks in Japan via SFA and DEA. Here, we first explain the
SFA approach and then the DEA approach.
Assume there are K inputs and one output, and that the inputs and outputs are
related by a Cobb-Douglas type of production function, where the constant returns toscale is assumed.

Then, the stochastic production possibility frontier can be written as

the follows:
(4)
where

is the output of the i-th public hall in year t,
10is the k-th input of the i-thpublic hall in year ,is a standard disturbance term that is assumed to follow anormal distribution with mean 0 and variance, andnormal distribution with mean 0 and variance. In this model,

inefficiency. Until the null hypothesis of
Subtracting

is assumed to follow a half
is an indicator of=0, all public halls are efficient producers.

from both sides of equation (4) gives
(5)

where

is output after the removal of the stochastic noise. The technically efficient

input levels for producing,, can be calculated using (5) and the following

equation:
,
where

(6)

is the ratio of the observed value of the k-th input to the observed value ofthe first input.
If the production frontier function is given, a dual cost function can be obtained bysolving the cost minimization problem.

In the case of the Cobb-Douglas production

function, the dual cost function is given by:
,

(7)

,

,

(9)

,
where

(8)

(10)

is the optimum cost for the i-th public hall in year t, andis the observed

price of the k-th input factor for i-th public hall in year t. From equation (7) and
Shepard’s lemma, the following equation can be obtained.

,

11

(11)

whereis the productive efficient level of the k-th input. As a result, following

Farell (1957), technical efficiency, allocative efficiency, and productive efficiency can becalculated using the following equations:

3.3

,

(12)

,

(13)

.

(14)

Using DEA to Measure Efficiency

For the measurement of inefficiency using DEA, the input-orientated DEA model isused because a one output model is used in this study.

As a result, only the

input-orientated DEA model is explained in this paper.
For the case of Variable Return to Scale (VRS) cost minimization, theinput-orientated DEA model sets out to solve the following equations.

,

(15)

where

is an output vector for the i-th facility,

facility,is theoutput matrix for

input matrix for

inputs and allof constants and e1 is an

is an input vector for the i-th

outputs and all
facilities,

vector of ones.

is a scalar,In this case,facilities,

is theis avectoris an estimate oftechnical efficiency (TE).
Next, for the cost minimization DEA model the following equations are solved:
12

(16)
where

is a vector of input prices for the i-th public hall and(which is calculatedby the linear programming problem) is the cost-minimizing vector of input quantities
for the i-th facility, given the input prices

and the output levels.

The productive and allocative efficiencies of the i-th facility can be calculated asfollows:
,

(17)

.

(18)

DEA does not allow us to explicitly take into consideration the panel nature of the data,so this is one of the factors which might lead to different estimates of inefficiencies when
SFA and DEA are used.

3.4 Estimated Models
When the SFA is adopted, to allow for time variation in the model for inefficiency,
a Time Variant Decay (TVD) model defined in equation (20) is used in addition to a
Time Invariant (TI) model defined in equation (19).as follows are used:
TI Model(19)
TVD Model

13

(20)
where

is the number of events produced by the manager of the i-th public hall inyear t,is the quantity of capital used for events by the i-th public hall in year t,

is the quantity of labor used for events by the i-th public hall in year t,

isdummy variable taking the value of 1 if at time

the public hall

DMS, and 0 otherwise,

In equation (19), ui is a measure ofis standard disturbance.

technical inefficiency, and in equation (20)can be seen from the model relating

is a measure of technical inefficiency. As

and ui in equation (20), this relationship allows

for changes in efficiency over time. If
If the null hypothesis of

has adopted the, equation (20) collapses to equation (19).

is accepted, there is no inefficiency. In this case, thefixed-effects and random-effects models are also estimated. By the way, in testingwhether the variance of η is zero or not, we need to be aware that under the null
hypothesis that the variance of η is zero, the parameter is on the boundary of theparameter space, so that Wald tests and Likelihood ratio tests of the null hypothesis do
not have standard chi-square distributions.

However, even when we take account ofAndrews' [2001] results, we find that the null hypothesis that the variance of η is zero isclearly rejected. When the DEA is used, the input-orientated Variable Returns to Scale(VRS) model is used (see, Nakayama (2002) for an example).

4. Data
The data used in this paper was obtained utilizing the provisions of Japan’sFreedom of Information Laws, namely, the ‘‘Act on Access to Information Held byAdministrative Agencies’ (Gyousei kikan no hoyuu suru jouhou no koukai ni kansuru

houritsu) and ‘Organs Law Concerning Access to Information held by Incorporated
Administrative Agencies, Etc.’ (Dokuritsu gyousei houjin nado no hoyuu suru jouhou nokoukai ni kan suru houritu)],. This laws create a system that provides guaranteedaccess to certain information held by the public sector (Jouhou koukai seido). The dataon Local governments whose financial power is weak tend to limit the people who canmake use of the freedom of information procedures to people who have lived in theirown local government area. When the author was not qualified to access the relevant
information, the information was requested by questionnaires.
Rather than requesting data on every public hall in Japan, around 2000
institutions, requests were made to the appropriate local government authorities for14

information on 200 randomly chosen public halls. The sample of 200 is roughly 10 % of
the total number of public halls in Japan. As a result of the freedom of information
requests, an unbalanced panel data set consisting of annual data from 2004 to 2009 on
these 200 public halls could be constructed.
In order to estimate the quantity of capital from the data provided, it wasnecessary to have a measure of the cost of capital,. Two definitions of the cost of capitalare employed.

The first is the Usercost (UC) of the building defined as
,

where

is the usercost,depreciation, andis the interest rate for loan payments,(24)
is the rate ofis the rate of increase of the value of land (Koujitika). The

second definition of the cost of capital comes from the Total Average of the Price
Indicator of Service for Corporations except Consumption Tax (Shouhizei wo nozoku

kigyoumuke service kakaku shisu no souheikin). Table 3 reports descriptive statistics
for two cases, when the price of capital is estimated using the usercost concept, andwhen the price of capital is estimated using the price indicator of services.
of capital,

The number

is calculated by.

There are three main problems that need to be considered when efficiency
indicators are applied to public halls.

The first problem is how the “output” of publichalls should be defined. Throsby and Withers (1979) refer to the difficulties in defining
the output of the performing arts.
is used in this paper.

One of the Throsby and Withers (1979)’s definitions

In theory, hall rentals and the number of events offered could beconsidered to be the two main measurable outputs of Japanese public halls. In thispaper, estimates of inefficiencies using the number of events are reported because
detailed data on hall rentals are not available.

The second difficulty is how to treat

temporary employees and volunteers which are a characteristic of the public sectors.
In the case of Japanese public halls from 2004 to 2009, it is assumed that the level of
temporary employees and volunteers is negligible, because they are not substitutable
for regular staff (see, for example, the survey of Research Institute of Industry andRegional Economy (2006)).

Figure 3 shows that 60.9 % of public halls used novolunteers in 2007. Though 21.6 % of public halls used volunteers constantly (Figure5), the main tasks of volunteers are as receptionists, ushers, or the staff in halls (seeFigure 4).

The third problem is how to standardize the balance sheets of public halls

as individual public halls have various formats for their balance sheets. If inputs are
simply divided into capital and labor, all balance sheets can be standardized.
15

Figure 3 Details of Public Hall Usage of Volunteers

no answer or
not known

using
volunteer
constantly

no volunteer

using
volunteer but
notconstantly

The total number of public halls which supply cultural events is 1211.
Source: as for Table 1

Figure 4: The Kinds of the Works for the Regular Volunteers

participation in planningparticipation in production
marketingstage lighting or sound support

Percentage

receptionist, guide, hall staff
costumes making or the stage settingotherno answer and not known

050

The total sample size is 262.
Source: as for Table 1

16

100

Table 3: Descriptive Statistics
r=usercost
Variable

Total

With DMS

Without DMS

wL

88882.77

103231.8080980.39

rK1

84140.73

89721.32

81067.36

w

6677.322

6708.661

6660.063

L

14.16817.18412.507

r1

0.126

0.102

0.140

K1

1290880

1925996941106.1

Q

26.86

36.76

21.399Sample Size

214

76

138

Variable

Total

With DMS

Without DMS

wL83476.26

31367.21

75115.57

rK271781.61

1575.068

70303.49w

6293.214

2828.724

6336.095

L

14.02617.56511.90625

r2

93.77493.79793.640K2

766.955

16.796752.800

Q

25.111

7.984

20.338Sample Size

232

62

160

r=price

Note: When the usercost is used to measure , the sample size is reduced because cases
where the usercost is estimated to be negative are dropped from the analysis.

5. Results and Discussion
STATA Version 10 was used to estimate the SFA models, and DEAP Version 2.1
developed by Coelli (1996) was used.to obtain the inefficiency estimates using the DEA
approach,
Table 4 and 5 present

estimates of the production function using the stochastic

frontier approach assuming Time Invariant inefficiency (TI) (Models 2, 5, 8, and 11) andTime Variant Decay (TVD) inefficiency (Models 3, 6, and 9),17estimates of theproduction function assuming fixed effects (Models 1, 4, 7, and 10).

These panel

models which do not explicitly include inefficiency terms may be more suitable than
SFA models when the tests for inefficiencies in the SFA model suggest there are no
inefficiencies. If the existence of inefficiency is accepted, TI SFA or TVD SFA model aresupported.
Examining the results for the parametric models in Table 5 indicates that withthe exception of the coefficients in the fixed effect model, all the estimated coefficientsassociated with the two inputs are positive.
estimated coefficients ofIn all the fixed effect models, theare negative, but not statistically significant.

These

results suggest the fixed effect model does not provide good estimates of the production
function, or that labor is irrelevant for the purposes of changing output.
Models 1-6 contain the DMS dummy variables to examine whether or not the
production function for public halls shifts for those halls introducing the DMS, while
Models 7-12 do not contain the DMS dummy variables. In all models containing the
DMS dummy, the estimated coefficients of the DMS dummy are positive and significant.
This suggests that the introduction of the DMS seems to have shifted the production
frontier outwards, that is, more output is achieved for the same inputs of labor andcapital as a result of introducing the DMS.
When the results for the TI and TVD models are compared, the TI model appears
to be the more acceptable model. The results for Models 3, 6 and 9 suggest that the TI
models are supported because the estimates ofare all statistically insignificant.

Therefore, Models 8 and 11 are used to compare the estimates of the three efficiency
indicators.

In order to measure the impact of the DMS as the inefficiency terms, themodel without the DMS dummy are used here. Given the different definitions of theprice of capital, the models using different estimates of the level of capital are
non-nested. In choosing between these models, it should be noted that the estimatedskewness of, 3.70 where price is used is closer to the skewness of half-normal

distribution assumed, 3.36, than the estimated skewness of, 4.34, when usercost is

used as the data for the price of capital (Table 7). Because the distribution of theinefficiency term has strong assumption, the model which has more relaxed assumption
is considered more appropriate. Therefore, Model 11 used for the calculation of threeefficiency terms.
The estimates of the efficiency indicators for both the SFA (Model 11) and DEA
approaches are shown in Table 6. The estimates for ‘Total’ are the average efficiency
estimates for all public halls at all points in time. The estimates for ‘With the DMS’and ‘Without the DMS’ are, respectively, the average efficiency estimates for all the18

public halls after they introduced the DMS, and the average efficiency estimates for the
public halls that did not introduce the DMS and public halls before they introduced the
DMS. The results obtained for the SFA method using different estimates ofconsistent except Productive Efficiency (PE).

are

Estimates of Technical Efficiency (TE)and Allocative Efficiency (AE) obtained using DEA are consistent with the estimates ofTE and AE obtained using SFA and support the robustness of the SFA-based estimation.
The results in Table 6 suggest that after the introduction of the DMS Technical
Efficiency (TE) worsened, while Allocative Efficiency (AE) improved after the
introduction of the DMS. Productive Efficiency (PE), the total effect of TE and AE,
remained in the result of SFA, while PE worsened in the result of DEA. There is no
doubt that Productive Efficiency (PE) did not improve.

One reason for the worseningof Technical Efficiency may be that the facilities that have introduced the DMS tended
to spend more on each event. On the other hand, steps to cut labor costs step by step
may have contributed to improvements in Allocative Efficiency.

Table 4: Results for Stochastic Frontier Analysis:r=usercost

Model 1Model 2Model 3Model 4Model 5Model 6

Fixed-Effects

TI

TVD

Fixed-effects

TI

TVD

lnK2

-0.008

0.021

0.028

0.072

0.132

0.132

(r=price)(0.029)(0.028)*(0.028)*(0.066)(0.050)(0.048)*lnL-0.136

0.284

0.265

-0.110

0.199

0.191

(0.168)(0.111)**(0.113)**(0.162)(0.110)*(0.111)*

3.025

4.833

4.697

2.548

4.363

4.342

(0.523)***(0.819)***(0.585)***(0.525)***(0.590)***(0.479)***

0.102

0.141

0.172

0.115

0.160

0.177

(0.056)*(0.055)***(0.061)***(0.057)**(0.052)***(0.060)***

3.087

3.038

2.860

(0.730)***(0.434)***(0.518)***Estimation
Methodconstant

dms-0.00619

2.839(0.393)***-0.003

(0.005)
Log likelihood-101.389

Prob > chi2

(0.005)-100.695
0.004-105.951
0.003-105.794

0.000

0.000

Notes:(1)For each variable, the first line is the coefficient estimate, and the second line is thestandard error.
(2)*, ** and *** denote significance at the 10%, 5% and 1% levels, respectively.

Table 5: Results for Stochastic Frontier Analysis: r=price
Model 7

Model 9Model 10

Fixed-Effects TI

TVD

Fixed-effects TI

lnK2

0.072

0.132

0.132

0.029

0.038

(r=price)-0.066(0.050)*(0.048)*-0.063-0.027

lnL

-0.11

0.199

0.191

-0.2130.23-0.162(0.110)*(0.111)*-0.155(0.113)**

2.548

4.363

4.342

3.032

4.78

(0.525)***(0.590)*** (0.479)*** (0.471)***

0.115

0.16

(0.057)**(0.052)*** (0.060)***Estimation
Methodconstant

dms

Model 82.86

Model 11(0.779)***

0.177

2.839

(0.518)*** (0.393)***3.07(0.680)***-0.003-0.005Log likelihood-105.951-105.794-104.664

Prob > chi2

0.000

0.000

0.041

Note: As for Table 5.

20

Table 6: Results for Measuring Efficiency via SFA model and VRS DEA model
r=usercost
SFA

DEA (VRS)

TE

AE

PE

TE

AE

PE

Mean

0.156

0.296

0.019

0.289

0.812

0.229

Standard Deviation

0.011

0.028

0.000

0.018

0.013

0.015

With

Mean

0.108

0.364

0.018

0.435

0.775

0.335

the DMS

Standard Deviation

0.014

0.032

0.001

0.034

0.021

0.030

Without

Mean

0.182

0.258

0.020

0.208

0.833

0.171

the DMS

Standard Deviation

0.014

0.039

0.000

0.016

0.017

0.014

Total

r=price
SFA

DEA (VRS)

TE

AE

PE

TE

AE

PE

Mean

0.152

0.388

0.022

0.306

0.820

0.241

Standard Deviation

0.010

0.049

0.001

0.017

0.013

0.014

With

Mean

0.106

0.465

0.022

0.219

0.841

0.180

the DMS

Standard Deviation

0.013

0.037

0.001

0.023

0.019

0.019

Without

Mean

0.180

0.341

0.022

0.359

0.808

0.278

the DMS

Standard Deviation

0.014

0.075

0.001

0.023

0.018

0.019

decreaseincreaseremaindecreaseincreasedecrease

Total

Changes by the DMS

Table 7: Skewness and Kurtosis of the Technical Efficiencies Estimated by SFA
Skewness of ur=usercost

4.339

r=price

3.696

6. Conclusion
There is a variety of anecdotal evidence from the managers of art related
facilities concerning the various changes that occurred after introducing of the DMS,
but it is too difficult to find any consistent results from this evidence. In order toassess the impact of the introduction of the DMS a random sample of roughly 20% of
21the population of public halls are used.

The results of this analysis suggest that the

introduction of the DMS did lead to an upward shift of the production frontier, but it
did not lead to any major changes in the efficiency of production. To be specific, after
the introduction of the DMS, Technical Efficiency decreased, Allocative Efficiency
increased, and Productive Efficiency did not improved. As a result, it appears thatthe DMS has contributed to some facilities cutting costs. These results suggest thatthe DMS contributes to improving efficiency of firms that were already near the
production frontier. The results also suggest that technical inefficiency is caused by
the characteristics of the individual facilities. One possible reason for this is that only
limited changes have been implemented carried out so far. Another possible reason isthat the DMS does not work well on some facilities which are in the urban areas.
While the DMS has improved the output of firms close to the production frontier, it has
not contributed to reducing the inefficiency of inefficient public halls. It seems thatan alternative system is needed to improve the efficiencies of these inefficient publichalls.

22

APPENDIX
A. The Relationship between Public Financial Power and their Selection of the DMS
It has implied by Kobayashi (2002) that local governments with weak public financial
positions would introduce the DMS to facilities under their control in order to reduce
their fiscal deficits, but the analysis that follows suggests that actually the reverse has
been observed, that is, local governments with strong public financial positions tend tohave introduced the DMS.
Assume the following the following probit model:
(A1)

(A2)

where

is an unobserved latent variable;

is dummy variable for the i-th

facility taking the value 1 if the i-th facility adopts the DMS and 0 otherwise;
FINPOWER is a measure of the financial power of the local government that is related
to the i-th facility; andis an error term that follows a standard normal distribution.

In order to estimate (A1) and (A2), cross-section data (2008) for on whether or not
the DMS has been introduced for a particular facility is available from the Public Hall
Data Base constructed by Japan Foundation for Regional Art-Activities in 2009; anddata on FINPOWER comes from the “financial status of local governments” in Ministry
Internal Affairs and Communications (Japan) (2008). The “financial status” of a local
government is an indicator that shows what proportion of their necessary costs in a year
can be self-financed. A ratio of less than unity indicates that the local government
needs to issue bonds in order to meet the difference between its costs and its revenues.
Figure 1 relates the proportion of halls that have introduced the DMS to the financial
status of the local government involved.
When estimating (A1) and (A2), exactly the same 200 facilities used in theoriginal panel dataset employed in Section 4 are used here. However, 20 facilities whichhave been established by prefectures are excluded from the analysis because thedefinition of “financial status” differs between prefectures, and cities.

For theremaining 180 facilities, the mean financial status is 0.68, with a minimum value of23

0.17 and a maximum value of 1.79 of these 180 facilities, had adopted the DMS.
The results of estimating equations (A1) and (A2) are:(0.000***) (0.000***)where the values in brackets are p-values, and N is the sample size. The estimatedcoefficient of FINPOWER is positive and strongly significant suggesting that local
governments with strong public financial positions have tended to introduce the DMS.
Figure 5: Proportion of Japanese Public Halls Introducing the DMS by Financial Status of
Local Government Authority

ratio
0.8

"ratio″ is the proportionof halls introducing the
DMS in Public Halls

0.7
0.6

Financial Status
Level
Level 1: 0.0-0.2
Level 2: 0.2-0.6
Level 3: 0.6-1.0
Level 4: 1.0-1.4
Level 5: 1.4-1.8

0.5
0.4
0.3
0.2
0.1
0
1

2

3

4

5

Financial Status Level

B. Commands for Calculating Efficiency Indicators Using STATA
When a Cobb-Duglas production function is assumed, the three efficiency indicators arecalculated in the following process, where ‘q’ is output, ‘r’ is price for capital, ‘w’ iswage, ‘K’ is the quantity of capital and ‘L’ is the quantity of labor.
1.

Choose the appropriate model, from the time invariant model or the time-varying
24decay model.

2.



xtfrontier lnY lnK lnL , ti

xtfrontier lnY lnK lnL , tvd

Compute estimates of technical efficiency which calculated automatically by the
Stata command.


3.

4.

Insert the estimated coefficients into the blanks.


gen b0=()--------constant

gen b1= ()--------coefficient for lnK

gen b2= ()--------coefficient fot lnL

Estimate ‘stochastic noise’ as:

5.

predict u, tegen v=lnY-b0-b1*lnK-b2*lnL+uCalculate the quantities of the technical efficient inputs.


gen s=k/l



gen Y=q

gen L_TE=(Y/((exp(b0 +v))*((s)^(b1))))^(-b1-b2)



gen K_TE=s*L_TE

25

6.

7.

Obtain the coefficients for the dual cost function.


gen delta_cons=(ln(b1+b2)-(b0 +ln(((b1)^(b1))*((b2)^(b2)))))/(b1+b2)



gen delta_K=(b1)/(b1+b2)



gen delta_L=(b2)/(b1+b2)



gen delta_Y=1/(b1+b2)

Calculate the productivity efficient total cost without stochastic noise, and thenobtain the efficiency indicators.


gen lnC=delta_cons+delta_K*ln(r)+delta_L*ln(w)+delta_Y*(lnY-v)



gen C_A=exp(lnC)

gen K_PE =delta_K*((r)^(-1))* C_A

gen L_PE=delta_L*((w)^(-1))*C_A

gen TE=(r* K_TE+w*L_TE)/(r*k+w*l)



gen AE=(r*K_PE+w*L_PE)/ (r*K_TE+w*L_TE)gen PE=(r*K_PE+w*L_PE)/(r*k+w*l)

26

REFERENCES
Aigner, D., Lovell C. A. K., and Schmidt P. (1977). Formulation and Estimation of Stochastic
Frontier Production Function Models, Journal of Econometrics, 6, 21-37.
Bergstrom, T., Blume L., Varian H. (1986). On the private provision of public goods. Journalof Public Economics, 29, 25-50.
Brooks, A. C., (1999). Nonprofit Firms in the Performing Arts, In Ginsburgh, V. A. (eds.),

Handbook of Art and Culture Volume.1, (Chapter 15), Amsterdam: North-Holland.
Coelli, T. J., (1996). A guide to DEAP version 2.1: a data envelopment analysis (computer)program. Centre of Efficiency and Productivity Analysis Working Paper, 96/08.
Cultural Policy Network (Bunkaseisaku Network) edi. (2004). What will change after the

introduction of the designated manager system? (Shiteikanrishaseido de Nani ga
kawarunoka), Tokyo: Suiyosha (in Japanese).
Farell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal

Statistical Society, A CXX (3), 253-290.
Globerman, S., and Book, S. H. (1974). Statistical cost functions for performing arts
organizations. Southern Economic Journal, 40, 668-671.
Goto, M. (2002). The panel data analysis for the measuring of the productive efficiency via
stochastic frontier model: Measuring of the efficiency of the electric industry especiallyelectricity

supplynetwork

section(Kakuritsuteki

Furonthia

ModeruniyoruSeisankouritsusei no Paneru Deta Bunseki: Wagakuni Denkizigyou Souhaiden
Nettowaku Bumon no Keisoku). Journal of the Japan Society of Public Utility Economics,
53 (3), 39-48 (in Japanese).
Halter, A. N., Carter, H. O., and Hocking, J. G. (1957). A note on the transcendental
production function. Journal of Farm Economics, 39, 966-974.
Hayashi, T. (1997). Project for public utility and deregulation. Tokyo: Toyo Keizai (inJapanese).
Honma, M. (1993). Economics of Philantholopy (Firansoropi no Keizaigaku). Tokyo: Toyo
Keizai (in Japanese).
James, E. (1983). How nonprofits grow: A model. Journal of Policy Analysis andManagement, 2 (3), 350-366.
Japan Foundation for Regional Art-Activities (2006) The condition of introducing designatedmanager system into Japanese local government: Survey of all over Japan and casestudies:SurveyandstudyreportinNovember,

2006.

(Heisei18

nendo

Shiteikanrisyaseido Dounyuzyoukyou Zittaichousa ), online PDF file (in Japanese)(http://www.jafra.or.jp/j/library/investigation/018/data/18_1.pdf)
Japan Foundation for Regional Art-Activities (2007), The actual situation of introducing

27

designated manager system into Japanese local government: Survey of all over Japanand case studies: Survey and study report in March, 2007 (Heisei 19 nendo
Shiteikanrisyaseido Dounyuzyoukyou Zittaichousa ), online PDF file (in Japanese)(http://www.jafra.or.jp/j/library/investigation/019/data/19_13.pdf)
Jaume, P. J. (2000). Partitioning input cost efficiency into its allocative and technicalcomponents: An empirical DEA application to hospitals. Socio-Economic Planning

Sciences, 34, 199-218.
Jorgenson, D. W. (1986). Econometric methods for modeling producer behavior. In Griliches,
Z. D., and Intriligator, M. D. (eds.), Handbook of Econometrics Volume.3, (Chapter 31),
Amsterdam: North-Holland.
Kobayashi, M. (2006). Designated manager system: Who does support the cultural publicity?

(Shirwikanrishaseido: Bunkatekikoukyousei wo sasaerunoha dareka). Tokyo: Jiji Press(in Japanese).
Kopp, R. J., and Diewert, W. E. (1982). The decomposition of frontier cost function deviations
into measures of technical and allocative efficiency. Journal of Econometrics, 19, 319-331.
Kuan, J. (2001). The phantom profits of the opera: Nonprofit ownership in the arts as a
make-buy decision. Journal of Law, Economics, and Organization, 17 (2), 507-520.
Last, A., and Wetzel, H. (2010). The efficiency of German public theaters: A stochastic
frontier analysis approach. Journal of Cultural Economics, 34, 89-110.
Maki, A. (2001). An Introduction to Applied Econometrics (Ouyou Keiryoukeizaigaku

Nyuumon). Tokyo: Nippon-Hyoron-sha (in Japanese).
Meeusen, W., and van den Broeck J. (1977). Efficiency estimation from Cobb-Douglas
production function with composed error, International Economic Review, 18, 435-444.
Nakagawa, I. (2001). The Japanese local government’s cultural policy for the times of adecentralization (Bunkenjizai no Bunkaseisaku). Tokyo: Keiso Shobo (in Japanese).
Nakagawa, I. and Matsumoto, S. (2007). How is the designated managers now?

(Shiteikanrisyaseido ha Ima dounatteirunoka). Suiyosha (in Japanese).
Nakaya, K. (ed.) (2005). An assessment of the policies for public halls (Koukyou Houru no

Seisakuhyouka). Tokyo: Keio University Press (in Japanese).
Nakayama, N. (2002). Measuring the economic efficiency of the Japanese water service
industries (Suidouzigyou no Keizaikouritsusei no Keisoku). Japanese Economic Study,
45, 23-40 (in Japanese).
Reichmann, G. (2004). Measuring university library efficiency using data envelopment
analysis. Libli, 54, 136-146.
Steinberg, R. (1986). The revealed objective functions of nonprofit firms. Rand Journal of

Economics, 17 (4), 508-526.
28

Taalas, M. (1997). Generalised cost functions for producers of performing arts: Allocative
inefficiencies and scale economies in theatres. Journal of Cultural Economics. 21(19),335-353.
Tachiki, S. (1999). Contemporary Japanese public halls and theaters (Gendai no

Koukyouhouru to Gekizyou). Tokyo: Sojinsha (in Japanese).
Tamura, H. (2002). Assessment for the Japanese public libraries and the data envelopment
analysis (Kouritsu Tosyokan no Kouritsusei no Hyoka to Hourakubunsekihou). Journalof Japan Society of Library and Information Science, 47 (4), 145-162 (in Japanese).
Throsby, C. D., and Withers, G. A. (1979). The economics of performing arts. New York: St.
Martins.
West, E. G. (1987). Nonprofit versus profit firms in the performing arts. Journal of Cultural

Economics, 11 (2), 37-48.
Yamashita, K. Akai, N. and Sato, M. (2002). Incentive effect lying the system which tax
revenue are allocated to local governments: Verification of the soft budget problem via
frontier cost function (Chihoukoufuzeiseido ni hisomu Incentive Kouka: Frontier

Hiyoukansuu niyoru Sofutona Yosanseiyakumondai no Kensyou ). Financial Review, 61,
120-145 (in Japanese).

29